High-performance computing relies heavily on parallel and distributed systems, which promptes us to establish both qualitative and quantitative criteria to assess the fault tolerability and vulnerability of the system’s underlying interconnection networks. Consider the scenario in which large-scale link failures split the interconnection network into several components and each processor has multiple good neighboring processors. In this scenario, the fault tolerability of the system can be measured by g-good-neighbor r-component edge-connectivity, denoted by \(\lambda _{g,r}(G)\) , which is defined as the minimum number of edges whose removal results in a disconnected network with at least r connected components and each vertex has at least g good neighbors. It combines the strategies of g-good-neighbor edge-connectivity and component edge-connectivity. In this paper, the g-good-neighbor \((r+1)\) -component edge-connectivity of 3-ary n-cube is investigated. This work is the first attempt enhancing link fault tolerability for 3-ary n-cube under double constraints in the presence of the large-scale faulty links, which breaks down the inherent idea that poses one limitation on the resulting network. In addition, our results cover the work of Xu et al. (IEEE Trans Reliab, 71(3):1230–1240, 2022) and Li et al. (J Parallel Distrib Comput, 27:104886, 2024). Finally, the compared results reveal that the g-good-neighbor \((r+1)\) -component edge-connectivity is almost r times the size of g-good-neighbor edge-connectivity and much larger than \((r+1)\) -component edge-connectivity in 3-ary n-cube.
